# On the nature of the Møller - Plesset critical point

*Alexey V. Sergeev, David Z. Goodson, Steven E. Wheeler, and Wesley D. Allen*

## Abstract

It has been suggested [F. H. Stillinger, J. Chem. Phys. 112, 9711
(2000)] that the convergence or divergence of Møller-Plesset
perturbation theory is determined by a critical point at a negative
value of the perturbation parameter z at which an electron cluster
dissociates from the nuclei. This conjecture is examined using
configuration-interaction computations as a function of z and using a
quadratic approximant analysis of the high-order perturbation series.
Results are presented for the He, Ne, and Ar atoms and the hydrogen
fluoride molecule. The original theoretical analysis used the true
Hamiltonian without the approximation of a finite basis set. In
practice, the singularity structure depends strongly on the choice of
basis set. Standard basis sets cannot model dissociation to an electron
cluster, but if the basis includes diffuse functions then it can model
another critical point corresponding to complete dissociation of all
the valence electrons. This point is farther from the origin of the z
plane than is the critical point for the electron cluster, but it is
still close enough to cause divergence of the perturbation series. For
the hydrogen fluoride molecule a critical point is present even without
diffuse functions. The basis functions centered on the H atom are far
enough from the F atom to model the escape of electrons away from the
fluorine end of the molecule. For the Ar atom a critical point for a
one-electron ionization, which was not previously predicted, seems to be
present at a positive value of the perturbation parameter. Implications
of the existence of critical points for quantum-chemical applications
are discussed.

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Results of work at UMassD

Designed by A. Sergeev.